The search for a permanent electron electric dipole moment (eEDM) serves as a test of fundamental symmetry violations and of physics beyond the Standard Model. Trapped molecular ions in the 3Δ1 metastable electronic state are suitable candidates for an eEDM search due to their large effective electric fields and long electron spin coherence times. This thesis presents the quantum state manipulation and coherent spectroscopy of trapped HfF+ molecular ions in rotating bias fields for an eEDM search. The quantum state manipulation, which involves preparation of a large fraction of molecular ions in a single desired quantum state as well as rotational-state resolved detection, is complicated by the lack of HfF+ spectroscopic information prior to the start of this thesis. We performed state preparation by first state-selectively autoionizing neutral HfF such that 35% of the HfF+ are formed in a single rovibrational level of the electronic ground state 1∑+, and then transferring those ions into the desired Stark levels of a single hyperfinerovibrational manifold of the 3Δ1 state. Rotational-state-resolved detection is accomplished by both laser-induced fluorescence and resonance-enhanced multi-photon photodissociation, where the latter is preferred as the state detection method of choice because its efficiency is two orders of magnitude higher compared to fluorescence. With the quantum state manipulation techniques developed, we performed Ramsey spectroscopy of the trapped HfF+ ions in the presence of rotating bias electric and magnetic fields, demonstrating electron spin coherence times as long as 150 ms. Finally, we present a preliminary measurement of the eEDM at the |de| < 10−25 e cm level.

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